Đáp án:
`S={2;6}`
Giải thích các bước giải:
`(x^2)/3+(48)/(x^2)=5(x/3+4/x)(ĐKXĐ:x\ne 0)`
`<=>(x^4+144)/(3x^2)=5(x(x^2+12)/(3x^2))`
`<=>x^4+144=5x^3+60x`
`<=>x^4-5x^3-60x+144=0`
`<=>x^4-2x^3-3x^3+6x^2-6x^2+12x-72x+144=0`
`<=>x^3(x-2)-3x^2(x-2)-6x(x-2)-72(x-2)=0`
`<=>(x-2)(x^3-3x^2-6x-72)=0`
`<=>(x-2)(x^3-6x^2+3x^2-18x+12x-72)=0`
`<=>(x-2)[x^2(x-6)+3x(x-6)+12(x-6)]=0`
`<=>(x-2)(x-6)(x^2+3x+12)=0`
`<=>`\(\left[ \begin{array}{l}x-2=0\\x-6=0\end{array} \right.\)`(Vì x^2+3x+12 \ne0)`
`<=>`\(\left[ \begin{array}{l}x=2(t/m)\\x=6(t/m)\end{array} \right.\)
Vậy `S={2;6}`
